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Synchronous Rendezvous for Location-Aware Agents

Andrew Collins 1 Jurek Czyzowicz 2 Leszek Gasieniec 1 Adrian Kosowski 3, 4 Martin A. Russell 1 
3 CEPAGE - Algorithmics for computationally intensive applications over wide scale distributed platforms
Université Sciences et Technologies - Bordeaux 1, Inria Bordeaux - Sud-Ouest, École Nationale Supérieure d'Électronique, Informatique et Radiocommunications de Bordeaux (ENSEIRB), CNRS - Centre National de la Recherche Scientifique : UMR5800
Abstract : We study rendezvous of two anonymous agents, where each agent knows its own initial position in the environment. Their task is to meet each other as quickly as possible. The time of the rendezvous is measured by the number of synchronous rounds that agents need to use in the worst case in order to meet. In each round, an agent may make a simple move or it may stay motionless. We consider two types of environments, finite or infinite graphs and Euclidean spaces. A simple move traverses a single edge (in a graph) or at most a unit distance (in Euclidean space). The rendezvous consists in visiting by both agents the same point of the environment simultaneously (in the same round). In this paper, we propose several asymptotically optimal rendezvous algorithms. In particular, we show that in the line and trees as well as in multi-dimensional Euclidean spaces and grids the agents can rendezvous in time O(d), where d is the distance between the initial positions of the agents. The problem of location-aware rendezvous was studied before in the asynchronous model for Euclidean spaces and multi-dimensional grids, where the emphasis was on the length of the adopted rendezvous trajectory. We point out that, contrary to the asynchronous case, where the cost of rendezvous is dominated by the size of potentially large neighborhoods, the agents are able to meet in all graphs of at most n nodes in time almost linear in d, namely, O(d log^2 n). We also determine an infinite family of graphs in which synchronized rendezvous takes time Ω(d).
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https://hal.inria.fr/hal-00646907
Contributor : Adrian Kosowski Connect in order to contact the contributor
Submitted on : Thursday, December 1, 2011 - 12:25:16 AM
Last modification on : Saturday, June 25, 2022 - 8:29:33 PM

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Andrew Collins, Jurek Czyzowicz, Leszek Gasieniec, Adrian Kosowski, Martin A. Russell. Synchronous Rendezvous for Location-Aware Agents. DISC 2011 - 25th International Symposium on Distributed Computing, Sep 2011, Rome, Italy. pp.447-459, ⟨10.1007/978-3-642-24100-0_42⟩. ⟨hal-00646907⟩

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